The invention relates to determining the lead required in shooting a projectile at a moving target and more particularly to a slide calculator for making such a determination.
It is well known that in order to hit a moving target such as skeet or game with a projectile, the projectile must be directed at a point ahead of the target location at the time the projectile is released. (The term "target" as used herein is intended to describe any moving object, living or inanimate, at which a shooter is aiming and therefore includes game.) The required distance ahead of the target is known as "lead" and the required amount of lead may be calculated from a knowledge of the directed velocity of the target, the directed velocity of the projectile and the distance from the shooter to the target at the time of shooting. The general formula for lead as a function of these variables is quite complex. However, for many applications a good approximation of the lead may be calculated by assuming that the velocity of the target and the projectile remain constant in magnitude and direction and that the distance from the shooter to the target does not change during the time of flight of the projectile. The later approximation is unnecessary if the distance measurement utilized is that from the shooter to the target at the time the projectile reaches the target. With these approximations the lead is given by the following formula: EQU L=(St.times.D)/Sp
where
St=target speed PA1 Sp=projectile speed PA1 D=distance to target
In order that the formula be accurately applied the shooter must be able to estimate leads for the range of target speeds, target ranges and projectile speeds which he is likely to encounter. Leads appropriate for different circumstances may be learned with the use of the above formula. However, for many persons use of the formula may be difficult and overly time consuming. Its direct use requires a knowledge of mathematics which many shooters do not have. Furthermore, while this formula appears to be simple enough its use requires that all of the speed and distance values be expressed in the same units of speed and distance. However, it is common in the English-speaking nations to think of the speed of a target such as skeet or game in miles per hour, to think of range in yards, and to express firearm projectile velocities in feet per second. A shooter, thinking of speeds and distance in these units of measurement must first convert target speed to feet per second and range to feet, before calculating the lead in units of feet by use of the mathematical formula. This requirement substantially increases the difficulty and time required for the calculation. Another problem in determining lead encountered by many shooters, especially inexperienced game hunters is to relate the type of motion of game (e.g., walk, trot, run, fly) to a particular speed of the game or to relate the type of projectile being fired (e.g. arrow, shotgun pellets, rifle bullet) to the speed of the projectile.
These difficulties may be overcome by use of the present invention. In accordance with the principal embodiments of the invention, cooperating logarithmic scales with indicia corresponding to the parameters target speed, range, projectile speed and lead are horizontally or circularly displayed on a horizontal or circular slide rule type device, the particular indicia and scale units being those most commonly known for the particular parameter. In three embodiments of the invention the target speed and target range scales are disposed on the fixed member; the projectile speed and lead scales are disposed on the movable slide member. In a fourth embodiment all of these scales are disposed on the fixed member and a separate reference scale is disposed on the slide member. Calculation of required lead is ordinarily accomplished in two slide steps. The target speed is first multiplied by the range and the result is divided by the projectile speed to obtain the required lead as will be more fully explained in the detailed description below. In this way the required speed may be quickly and easily calculated without any conversion of units and requirements or mathematical knowledge. The calculation may of course also be made by dividing the target range or target speed by the projectile speed first, before the multiplication step (provided the scales are appropriately rearranged).
The calculation in each of the embodiments may be used in a number of shooting situations. These include game hunting, and skeet or target shooting as well as in military applications such as in shooting at various moving military targets.
In accordance with another feature of the invention pictorial markers representative of various projectiles which are commonly utilized, e.g. arrows, shot and rifle bullets, are disposed along the projectile velocity scale at locations corresponding to their normal speed, so that the lead requirement for each of these projectiles may be calculated without knowledge of actual projectile speed.
In accordance with still another feature of the invention a verbal description of target (game) speed is disposed at appropriate locations along the target speed scale so that a game hunter need only know "mode" of movement, that game is, for example, "walking," "trotting," "running" or "flying," to be able to calculate (or at least estimate) required lead.
In many instances, where the projectile speed is known for a firearm which is repeatedly used, it is very useful to have a calculator specifically designed for calculating required lead for a single projectile speed, but requiring only one slide step to make the calculation. Such a fifth embodiment of the present invention will accomplish this result. In accordance with this embodiment, there are only three scales, two being disposed on a fixed member and one being disposed on a slide member. The two scales disposed on the fixed member are offset relative to each other by such an amount as corresponds to the particular projectile speed, thereby eliminating the requirement of a division step in the calculation of required lead. In accordance with another feature of the invention, one or more of the scales used in the fifth embodiment may be formed unattached to the fixed and slide members but may be removably attached to the fixed member by the user with an adhesive at a location corresponding to the projectile speed of his particular weapon. This embodiment of the invention could be made very small, for example 1" by 5", and could be mounted directly on the particular weapon for convenient use during a hunting situation.